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Shortcuts for Windows Installer applications are not regular shortcuts.
Instead of containing full paths to .exes or other type of files, they contain objects called "descriptors." A descriptor is a compressed representation of a {Product-Code, Feature Key, Component Code} triple.

When you click on a Windows Installer shortcut, the Windows shell uses the data in the descriptor to call the MsiProvideComponent function. Look at the Microsoft Windows Installer Help file for MsiProvideComponent, and note that it takes a Product Code, a Feature Key, and a Component Code and returns a path for that component. In the process of doing that, the API verifies that all of the components that are part of the specified feature have a valid keypath on the computer (the key files exists), and it does any installations necessary to get all the components there if any of them are missing by using the MsiConfigureFeature function. Then the shell gets a path back, which it uses the ShellExecute function to execute the process.